A Fast Sparse Block Circulant Matrix Vector Product

In the context of computed tomography (CT), iterative image reconstruction techniques are gaining attention because high-quality images are becoming computationally feasible. They involve the solution of large systems of equations, whose cost is dominated by the sparse matrix vector product (SpMV). Our work considers the case of the sparse matrices being block circulant, which arises when taking advantage of the rotational symmetry in the tomographic system. Besides the straightforward storage saving, we exploit the circulant structure to rewrite the poor-performance SpMVs into a high-performance product between sparse and dense matrices. This paper describes the implementations developed for multi-core CPUs and GPUs, and presents experimental results with typical CT matrices. The presented approach is up to ten times faster than without exploiting the circulant structure.